Ranked Pairs TB

Violation of Semi-Positive Involvement

Profile type: Profile
Config: 4 c, 8 v
Parameters: ∅

Semi-Positive Involvement violation found:
Original profile:
+---+---+---+---+---+
| 2 | 1 | 1 | 3 | 1 |
+---+---+---+---+---+
| 1 | 2 | 2 | 3 | 3 |
| 3 | 0 | 1 | 0 | 2 |
| 2 | 1 | 3 | 1 | 1 |
| 0 | 3 | 0 | 2 | 0 |
+---+---+---+---+---+
Profile([[1, 3, 2, 0], [2, 0, 1, 3], [2, 1, 3, 0], [3, 0, 1, 2], [3, 2, 1, 0]], rcounts=[2, 1, 1, 3, 1], cmap={0: '0', 1: '1', 2: '2', 3: '3'})
Ranked Pairs TB winner is {1}

Profile with ballot removed:
+---+---+---+---+---+---+---+
| 1 | 1 | 1 | 1 | 1 | 1 | 1 |
+---+---+---+---+---+---+---+
| 1 | 1 | 2 | 2 | 3 | 3 | 3 |
| 3 | 3 | 0 | 1 | 0 | 0 | 0 |
| 2 | 2 | 1 | 3 | 1 | 1 | 1 |
| 0 | 0 | 3 | 0 | 2 | 2 | 2 |
+---+---+---+---+---+---+---+
Profile([[1, 3, 2, 0], [1, 3, 2, 0], [2, 0, 1, 3], [2, 1, 3, 0], [3, 0, 1, 2], [3, 0, 1, 2], [3, 0, 1, 2]], rcounts=[1, 1, 1, 1, 1, 1, 1], cmap={0: '0', 1: '1', 2: '2', 3: '3'})
Ranked Pairs TB winner is {3}

Margin graph of profile with ballot removed:
Winners: [3]

Truncated ballot: {3: 1, 2: 2}
Top-ranked candidate: 3
Ranked candidates: (3, 2)
Unranked candidates: [0, 1]

Profile with truncated ballot:
+---+---+---+---+---+---+---+---+
| 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
+---+---+---+---+---+---+---+---+
| 1 | 1 | 2 | 2 | 3 | 3 | 3 | 3 |
| 3 | 3 | 0 | 1 | 0 | 0 | 0 | 2 |
| 2 | 2 | 1 | 3 | 1 | 1 | 1 |   |
| 0 | 0 | 3 | 0 | 2 | 2 | 2 |   |
+---+---+---+---+---+---+---+---+
ProfileWithTies([{1: 1, 3: 2, 2: 3, 0: 4}, {1: 1, 3: 2, 2: 3, 0: 4}, {2: 1, 0: 2, 1: 3, 3: 4}, {2: 1, 1: 2, 3: 3, 0: 4}, {3: 1, 0: 2, 1: 3, 2: 4}, {3: 1, 0: 2, 1: 3, 2: 4}, {3: 1, 0: 2, 1: 3, 2: 4}, {3: 1, 2: 2}], rcounts=[1, 1, 1, 1, 1, 1, 1, 1], cmap={0: '0', 1: '1', 2: '2', 3: '3'})
Ranked Pairs TB winner is {1}

Margin graph of profile with truncated ballot:
Winners: [1]

Winners shifted from including top-ranked candidate 3 to unranked candidates [1]